The interactions between electrons, phonons, and the lattice can result in one or more lattice, charge, spin, and orbital orders. These orders, and the competition between different states they generate, result in many interesting phenomena, such as magnetism, metal-to-insulator transition, giant magnetoresistance, superconductivity, heavy fermion behavior, etc. Here I report the research on three systems: Co2As1−xPx, FexTaS2, and Sr2Mn3As2O2, and the corresponding phenomena. In Co2As1−xPx, the magnetic properties are strongly correlated with their crystal structure. The P doping induces two structural phase transitions. The itinerant ferromagnetism in Co2As is enhanced by the first structural phase transition (x∼ 0.04) and quenched by the second structural phase transition (x between 0.85 and 0.90). In FexTaS2, I studied the correlation between magneto-transport properties and the Fe concentration x. When x deviates from the two commensurate values 1/4 and 1/3 where Fe ions form superstructures, both the spin misalignment and the magnetoresistance increase. The largest magnetoresistance that has been observed so far is 140% in Fe0.297TaS2, where the Fe concentration is close to the average of two commensurate values. In Sr2Mn3As2O2, I grew the first Sr2Mn3As2O2 single crystals and performed single crystal neutron scattering, which reveals that the magnetic structure at one of its layers has a quasi two-dimensional antiferromagnetic order. The energy dispersion of this magnetic order has linear dependence with wave momentum at the low energy transfer region, which is consistent with the spin wave of antiferromagnetic order. Additionally, band structure calculations indicate that Sr2Mn3As2O2 is an Mott insulator and the Mott transition is both layer- and orbital-selective, where the dx2−y2 orbital in this layer dominates the Mott transition.